3. OBSERVATIONS OF DISKS

The most extensive study of the photometric disk parameters in
the optical and near-IR is that of
a statistically complete sample of 86 disk dominated galaxies in
Roelof de Jong's thesis
(1995,
1996a,
b,
c;
de Jong & van der Kruit,
1994).
Some of his conclusions are:

Freeman's law is really an upper limit to the central surface
brightness.

The scalelength hR does not correlate with Hubble
type.

In disks fainter regions are generally bluer, probably
resulting from a combination of stellar age and metallicity gradients.

Figure 4. The radial scalelength
hR and vertical scaleheight
hz for a sample of 34 edge-on galaxies. Panels (a) and
(b) show the distribution (solid line is corrected for sample selection)
of hR and the correlation with the rotation
velocity. Panels (d) and (e) show the same for
hz and (c) and (f) for the ratio
hR / hz (after
Kregel et al.,
2001).

Figure 5. The relation between the
truncation radius Rmax and the radial scalelength
hR of the disks in a sample of edge-on
galaxies. The righthand panel shows the ratio
Rmax / hR as a function of
hR and the lines are models based on the formalism of
Dalcanton et al.,
1997
(from Kregel et al.,
2001).

Both hR and
hz correlate in general terms
with Vmax.

For hR this is expected from the Tully-Fisher
relation.

Our Galaxy would be somewhat unusual if the scalelength
hR
is as small as 2 to 2.5 kpc as some recent studies claim (see also
van der Kruit, 2000).

The flattening of the sample after volume correction is
hR / hz = 7.3 ± 2.2. Then

(21)

So most galaxies appear not to be "maximum disk". Recall that this
result follows directly from the observations using only the rotation
curve of the self-gravitating exponential disk, hydrostatic equilibrium
and Bottema's (empirical, but explainable) relation (8).
Bottema (1993)
derived a similar result in the analysis of his sample
of galaxies, in which he measured the stellar kinematics and found
Vdiskmax / Vmax = 0.63
± 0.17.

At least 20 of the spirals show radial truncations.

The ratio of the truncation radius and the scalelength is
Rmax / hR = 3.6 ± 0.6.

But large galaxies have smaller values for this ratio than
small ones.

For common disks with scalelengths of 5 kpc or less, the ratio
is about 4.

The truncation radius in a simple view results from the maximum
specific angular momentum of the sphere from which the disk collapsed.
Van der Kruit (1987),
in the context the
Fall & Efstathiou (1980)
picture of disk galaxy formation, then predicted a value of 4.5
for the ratio, based on a
Peebles (1971)
spin parameter
=
J|E|1/2G-1M-5/2 of 0.7.
Dalcanton et al.
(1997)
have extended this to a models with a dispersion in the spin parameter.
We have calculated model surface density profiles with their
method for
Mtot = 1010 - 1013M and
= 0.01 - 0.28. These are
the lines in Fig. 5b.

For completeness I mention that in many cases there is a warp in the
HI-layer in the outer parts, often starting roughly at the truncation
radius. This suggests that the warp material has been accreted subsequent
to disk formation.